# What is Sensitivity, Specificity, False positive, False negative?

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Sensitivity is a measure of how well a test can detect the presence of a disease or condition in a population. It is also known as the true positive rate (TPR), which means the proportion of people who have the disease and test positive for it. A high sensitivity means that the test can correctly identify most of the people who have the disease, and avoid missing or overlooking them. A low sensitivity means that the test can miss a lot of people who have the disease, and falsely classify them as negative. This can have serious consequences for their health and treatment.

Sensitivity is important for several reasons. First, it helps us to evaluate the accuracy and reliability of a test. A test with a high sensitivity can give us more confidence that it is not missing any cases of the disease, and that it is capturing the true prevalence of the disease in a population. A test with a low sensitivity can lead to underestimation of the disease burden, and misdiagnosis of many individuals.

Second, sensitivity helps us to choose the best test for a given purpose or situation. Depending on the type and severity of the disease, we may want to use a test with a high sensitivity to screen for it, especially if the disease is life-threatening or contagious. For example, in the case of COVID-19, we want to use a test with a high sensitivity to detect the infection as early as possible, and isolate and treat the infected individuals. A test with a low sensitivity can result in delayed diagnosis, increased transmission, and worse outcomes.

Third, sensitivity helps us to interpret the results of a test and make informed decisions based on them. A positive result from a test with a high sensitivity means that there is a high probability that the person has the disease, and that they need further confirmation or treatment. A negative result from a test with a high sensitivity means that there is a low probability that the person has the disease, and that they can be reassured or excluded from further testing. However, sensitivity is not the only factor that affects the interpretation of test results. We also need to consider specificity, false positive rate, false negative rate, positive predictive value, and negative predictive value, which we will discuss in later points.

In summary, sensitivity is a key indicator of how well a test can detect the presence of a disease or condition in a population. It is important for evaluating the accuracy and reliability of a test, choosing the best test for a given purpose or situation, and interpreting the results of a test and making informed decisions based on them.

The true positive rate (TPR) is a measure of how well a test can identify the presence of a condition or disease. It is also known as sensitivity, recall, or hit rate. It is calculated by dividing the number of true positives (TP) by the number of actual positives (AP), which is the sum of true positives and false negatives (FN). The formula is:

$$TPR = \frac{TP}{AP} = \frac{TP}{TP + FN}$$

A true positive is a test result that correctly indicates that a person has the condition or disease. A false negative is a test result that incorrectly indicates that a person does not have the condition or disease. The actual positives are the people who really have the condition or disease, regardless of their test results.

The TPR ranges from 0 to 1, where 0 means that the test never detects the condition or disease, and 1 means that the test always detects the condition or disease. A higher TPR indicates that the test is more sensitive and less likely to miss cases. A lower TPR indicates that the test is less sensitive and more likely to overlook cases.

For example, suppose we have a test for COVID-19 that has a TPR of 0.95. This means that out of 100 people who have COVID-19, the test will correctly identify 95 of them as positive and miss 5 of them as negative. The TPR tells us how well the test can detect COVID-19 among those who have it, but it does not tell us how well the test can rule out COVID-19 among those who do not have it. For that, we need another measure called specificity or true negative rate (TNR).

One of the screening tests for COVID-19 is the COVID-19 IgG/IgM diagnostic test, which detects the presence of antibodies to SARS-CoV-2, the virus that causes COVID-19, in blood samples. This test can help identify people who have been exposed to the virus or have recovered from the infection. However, this test cannot confirm the current infection status or the level of immunity.

The COVID-19 IgG/IgM diagnostic test is a lateral flow immunoassay that uses a device with a nitrocellulose strip coated with anti-human IgM and IgG antibodies and a control line. The device also contains a buffer solution and a blood lancet for fingerstick blood collection. The test procedure is as follows :

- Collect a blood sample from the finger using the lancet and transfer it to the sample well on the device using a pipette.
- Add two drops of buffer solution to the buffer well on the device.
- Wait for 15 minutes and read the results.

The results are interpreted by observing the presence or absence of colored lines on the test strip. The control line (C) should always appear to indicate that the test is valid. The IgM line (M) indicates the presence of IgM antibodies, which are usually produced early in the infection. The IgG line (G) indicates the presence of IgG antibodies, which are usually produced later in the infection and provide longer-term immunity.

The possible results are :

- Positive for IgM only: The sample contains IgM antibodies to SARS-CoV-2. This may indicate a recent or current infection.
- Positive for IgG only: The sample contains IgG antibodies to SARS-CoV-2. This may indicate a past infection or vaccination.
- Positive for both IgM and IgG: The sample contains both IgM and IgG antibodies to SARS-CoV-2. This may indicate a recent or current infection or a past infection with some residual IgM antibodies.
- Negative: The sample does not contain any detectable antibodies to SARS-CoV-2. This may indicate that the person has not been exposed to the virus or has not developed an immune response yet.
- Invalid: The control line does not appear. The test is invalid and should be repeated with a new device.

The COVID-19 IgG/IgM diagnostic test has a reported sensitivity of 95% and a specificity of 96%. However, the accuracy of the test may vary depending on several factors, such as the timing of the test, the quality of the sample, and the prevalence of the disease in the population. Therefore, it is important to interpret the results in conjunction with other clinical and epidemiological information and to confirm them with other types of tests if needed.

Specificity is the ability of a test to correctly identify those patients without the disease. It is also known as the True Negative Rate (TNR), i.e the percentage of healthy people who are correctly identified as not having the condition. A test that can identify all sample tests from healthy individuals to be negative is very specific.

Specificity is important for ruling in a disease, i.e. confirming that a person who tests positive actually has the disease. A test with high specificity will have a low rate of false positives, i.e. healthy people who are incorrectly identified as sick. False positives can cause unnecessary anxiety, stress, and further testing for the patients, as well as wasting resources and time for the health care system.

Specificity is also important for estimating the prevalence of a disease in a population, i.e. how common the disease is among a group of people. A test with high specificity will have a low rate of overestimating the prevalence of the disease, i.e. reporting more cases than there actually are. This can lead to inaccurate public health policies and interventions based on inflated numbers.

Specificity can be influenced by various factors, such as the quality of the test, the criteria for defining a positive result, and the characteristics of the population being tested. For example, a test that requires a high level of antibodies to be detected may have high specificity but low sensitivity, i.e. it may miss some cases of early or mild infection. Similarly, a test that is applied to a population with a low prevalence of the disease may have high specificity but low positive predictive value, i.e. it may have many false positives relative to true positives.

Therefore, specificity is one of the key indicators of the accuracy and usefulness of a test, along with sensitivity and other measures. A good test should have both high sensitivity and high specificity, but there is often a trade-off between them depending on the purpose and context of the testing.

The true negative rate (TNR) is another way of expressing the specificity of a test. It is the proportion of people who do not have the disease and are correctly identified as negative by the test. It is also known as the **specificity** of the test.

The TNR can be calculated by dividing the number of true negatives by the total number of people who do not have the disease. Alternatively, it can be calculated by subtracting the false positive rate (FPR) from 1.

TNR = True Negatives / (True Negatives + False Positives)

or

TNR = 1 - FPR

The TNR is important because it tells us how well the test can rule out the disease in people who are healthy. A high TNR means that the test is very accurate in excluding the disease, while a low TNR means that the test is prone to misclassify healthy people as having the disease.

For example, suppose we have a test for COVID-19 that has a TNR of 0.9. This means that 90% of people who do not have COVID-19 will test negative, while 10% will test positive. This also means that the FPR of the test is 0.1, which means that 10% of healthy people will be falsely diagnosed with COVID-19.

A high TNR is desirable for tests that are used to confirm the absence of a disease or to rule out a serious condition. For example, a test for HIV should have a high TNR to avoid false positives that can cause psychological distress and unnecessary treatment. A low TNR can lead to overdiagnosis and overtreatment, which can have negative consequences for both individuals and public health.

The TNR can vary depending on the prevalence of the disease in the population. The prevalence is the proportion of people who have the disease in a given group or area. A higher prevalence means that more people have the disease, while a lower prevalence means that fewer people have the disease.

The TNR can decrease when the prevalence increases, because more false positives will occur. Conversely, the TNR can increase when the prevalence decreases, because fewer false positives will occur. Therefore, it is important to consider the prevalence of the disease when interpreting the TNR of a test.

To summarize, the true negative rate (TNR) is a measure of how well a test can correctly identify people who do not have the disease. It is also known as specificity and it can be calculated by dividing the number of true negatives by the total number of people who do not have the disease or by subtracting the false positive rate from 1. A high TNR means that the test is very accurate in excluding the disease, while a low TNR means that the test is prone to misclassify healthy people as having the disease. The TNR can vary depending on the prevalence of the disease in the population.

A mnemonic is a memory aid that helps you remember something easily. One common mnemonic for sensitivity and specificity is **SnNouts** and **SpPins**.

**SnNout**: A test with a high sensitivity value (Sn) that, when negative (N), helps to rule out a disease (out).

**SpPin**: A test with a high specificity value (Sp) that, when positive (P) helps to rule in a disease (in).

Let`s see how this mnemonic works with an example. Suppose you have a test for COVID-19 that has a sensitivity of 95% and a specificity of 90%. This means that the test correctly identifies 95% of the people who have COVID-19 and 90% of the people who do not have COVID-19.

If you use this test on a person who has COVID-19, there is a 95% chance that the test will be positive and a 5% chance that the test will be negative. Therefore, a negative test result can help you rule out COVID-19 with high confidence, since it is unlikely that the person has the disease. This is what SnNout means.

If you use this test on a person who does not have COVID-19, there is a 90% chance that the test will be negative and a 10% chance that the test will be positive. Therefore, a positive test result can help you rule in COVID-19 with moderate confidence, since it is more likely that the person has the disease than not. This is what SpPin means.

However, keep in mind that sensitivity and specificity are not enough to determine the accuracy of a test. You also need to consider the prevalence of the disease in the population and the positive and negative predictive values of the test. These concepts will be explained in the next points.

The true/false refers to the assigned classification being correct or incorrect while positive/negative refers to the assignment to a positive or negative category of results.

These terminologies are dependent on the population subject to the test. Normally, when there is a disease outbreak, diagnostic tests are done to determine if an individual has the disease or not.

For persons who are sick, the test outcome is positive while those without the disease, the test outcome will be negative. But in some circumstances, the test results may not match the individual’s status, therefore they can be defined as:

**False-positive**: Healthy people incorrectly identified as sick**False-negative**: Sick people incorrectly identified as healthy.

A **false-positive** result means that the test indicates that a person has the disease when they actually do not. This can have negative consequences such as unnecessary anxiety, treatment, isolation, or further testing. A **false-negative** result means that the test indicates that a person does not have the disease when they actually do. This can have serious consequences such as delayed diagnosis, treatment, or transmission of the disease to others.

The rate of false-positive and false-negative results depends on the sensitivity and specificity of the test, as well as the prevalence of the disease in the population. A test with high sensitivity will have a low false-negative rate, while a test with high specificity will have a low false-positive rate. However, no test is perfect and there will always be some degree of error.

To reduce the risk of false-positive and false-negative results, it is important to use a reliable and validated test, to follow the instructions carefully, and to interpret the results in context with other clinical information. Sometimes, it may be necessary to repeat or confirm the test with another method to increase accuracy and confidence.

To illustrate how sensitivity and specificity can affect the interpretation of COVID-19 test results, let us consider a hypothetical scenario where we have a population of 10,000 people and we want to test them for SARS-CoV-2 infection using a PCR test and a serological test. We will assume that the prevalence of COVID-19 in this population is 5%, meaning that 500 people are actually infected and 9,500 are not. We will also assume that the PCR test has a sensitivity of 70% and a specificity of 95%, and that the serological test has a sensitivity of 90% and a specificity of 98%. These values are based on the lower end of current estimates from systematic reviews .

Using these parameters, we can calculate the expected number of true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN) for each test, as shown in Table 2.

Test | TP | FP | TN | FN |
---|---|---|---|---|

PCR | 350 | 475 | 9,025 | 150 |

Serology | 450 | 190 | 9,310 | 50 |

From these numbers, we can see that the PCR test correctly identifies 350 out of the 500 infected people (70% sensitivity), but also misclassifies 475 out of the 9,500 non-infected people as positive (5% false positive rate or 95% specificity). The serological test correctly identifies 450 out of the 500 infected people (90% sensitivity), but also misclassifies 190 out of the 9,500 non-infected people as positive (2% false positive rate or 98% specificity).

To evaluate the accuracy of each test, we can also calculate the positive predictive value (PPV) and the negative predictive value (NPV), which tell us the probability that a positive or negative test result is correct. The PPV and NPV depend not only on the sensitivity and specificity of the test, but also on the prevalence of the disease in the population. The formulas for PPV and NPV are:

PPV = TP / (TP + FP)

NPV = TN / (TN + FN)

Using these formulas, we can calculate the PPV and NPV for each test, as shown in Table 3.

Test | PPV | NPV |
---|---|---|

PCR | 42.4% | 98.4% |

Serology | 70.3% | 99.5% |

From these numbers, we can see that the PCR test has a low PPV of 42.4%, meaning that only about four out of every ten people who test positive are actually infected. This is because the PCR test has a relatively low specificity and a high false positive rate in a population with a low prevalence of COVID-19. On the other hand, the PCR test has a high NPV of 98.4%, meaning that almost all people who test negative are truly not infected. This is because the PCR test has a relatively high sensitivity and a low false negative rate in this population.

The serological test has a higher PPV of 70.3%, meaning that about seven out of every ten people who test positive are actually infected. This is because the serological test has a higher specificity and a lower false positive rate than the PCR test in this population. The serological test also has a higher NPV of 99.5%, meaning that almost all people who test negative are truly not infected. This is because the serological test has a higher sensitivity and a lower false negative rate than the PCR test in this population.

These results show that both tests have their advantages and limitations, depending on the purpose and context of testing. The PCR test is more useful for diagnosing acute infection and isolating cases, especially in symptomatic or exposed individuals, but it may also generate many false positives in low-prevalence settings. The serological test is more useful for detecting past infection and estimating immunity, especially in asymptomatic or recovered individuals, but it may also miss some early or mild infections.

Therefore, it is important to interpret COVID-19 test results with caution and consider other factors such as clinical symptoms, exposure history, epidemiological trends, and alternative diagnoses . A single test result may not be sufficient to confirm or exclude COVID-19, and repeat or confirmatory testing may be needed in some cases. Testing should always be accompanied by appropriate counseling, education, and infection prevention measures.

Sensitivity and specificity are two important measures of the accuracy of a diagnostic test. They can be calculated using the following formulas:

Sensitivity = (Number of true positives) / (Number of true positives + Number of false negatives)

Specificity = (Number of true negatives) / (Number of true negatives + Number of false positives)

To understand these formulas, let us first define some terms:

- A true positive is a person who has the disease and tests positive for it.
- A false positive is a person who does not have the disease but tests positive for it.
- A true negative is a person who does not have the disease and tests negative for it.
- A false negative is a person who has the disease but tests negative for it.

The denominator of the sensitivity formula is the total number of people who have the disease, regardless of their test results. The numerator is the number of people who have the disease and are correctly identified by the test. Therefore, sensitivity measures the proportion of people with the disease who are correctly detected by the test.

The denominator of the specificity formula is the total number of people who do not have the disease, regardless of their test results. The numerator is the number of people who do not have the disease and are correctly identified by the test. Therefore, specificity measures the proportion of people without the disease who are correctly excluded by the test.

To illustrate how to calculate sensitivity and specificity, let us use the example from point 8. We have a new rapid diagnostic test for COVID-19 that has been evaluated on 600 people, 480 of whom have the disease and 120 of whom do not. The results are shown in the table below:

Test Positive | Test Negative | Total | |
---|---|---|---|

Have Disease | 480 | 5 | 485 |

Do Not Have Disease | 15 | 100 | 115 |

Total | 495 | 105 | 600 |

Using the formulas above, we can calculate the sensitivity and specificity as follows:

Sensitivity = 480 / (480 + 5) = 0.99

Specificity = 100 / (100 + 15) = 0.87

This means that the test has a high sensitivity (99%) and a moderate specificity (87%). A high sensitivity means that the test is very good at detecting people who have COVID-19, while a moderate specificity means that the test is somewhat good at excluding people who do not have COVID-19. However, sensitivity and specificity are not enough to evaluate the performance of a diagnostic test. We also need to consider other measures, such as positive predictive value and negative predictive value, which will be discussed in point 10.

Positive predictive value (PPV) and negative predictive value (NPV) are two important measures that can help us interpret the results of a diagnostic test. They tell us how likely it is that a person who tests positive or negative actually has or does not have the disease.

PPV is the probability that a person who tests positive has the disease. It depends on the sensitivity and specificity of the test, as well as the prevalence of the disease in the population. A high PPV means that most of the positive results are true positives, and a low PPV means that many of the positive results are false positives.

NPV is the probability that a person who tests negative does not have the disease. It also depends on the sensitivity and specificity of the test, as well as the prevalence of the disease in the population. A high NPV means that most of the negative results are true negatives, and a low NPV means that many of the negative results are false negatives.

PPV and NPV are useful for evaluating the accuracy and reliability of a diagnostic test. They can help us decide how to act on the test results and whether to perform further testing or treatment. They can also help us compare different tests and choose the best one for a given situation. However, they are not fixed properties of a test, but vary depending on the population being tested and the prevalence of the disease. Therefore, they should be calculated and reported for each specific context and application.

Positive predictive value (PPV) and negative predictive value (NPV) are two important measures of the accuracy of a diagnostic test. They tell us how likely it is that a person who tests positive or negative for a disease actually has or does not have the disease.

To calculate PPV and NPV, we need to know four values:

- The number of true positives (TP), which are people who have the disease and test positive
- The number of false positives (FP), which are people who do not have the disease and test positive
- The number of true negatives (TN), which are people who do not have the disease and test negative
- The number of false negatives (FN), which are people who have the disease and test negative

We can use these values to construct a contingency table, which summarizes the results of the test:

Test Positive | Test Negative | Total | |
---|---|---|---|

Have Disease | TP | FN | TP+FN |

Do Not Have Disease | FP | TN | FP+TN |

Total | TP+FP | TN+FN | TP+FP+TN+FN |

The PPV is the proportion of people who test positive and have the disease, out of all people who test positive. It can be calculated by dividing TP by TP+FP:

$$PPV = \frac{TP}{TP+FP}$$

The NPV is the proportion of people who test negative and do not have the disease, out of all people who test negative. It can be calculated by dividing TN by TN+FN:

$$NPV = \frac{TN}{TN+FN}$$

PPV and NPV depend on the prevalence of the disease in the population, which is the proportion of people who have the disease. The higher the prevalence, the higher the PPV and the lower the NPV. The lower the prevalence, the lower the PPV and the higher the NPV.

To illustrate this, let us use an example of a COVID-19 diagnostic test that has a sensitivity of 95% and a specificity of 90%. This means that it correctly identifies 95% of people who have COVID-19 and 90% of people who do not have COVID-19. Let us assume that we apply this test to two different populations: one with a high prevalence of COVID-19 (10%) and one with a low prevalence of COVID-19 (1%).

In the high prevalence population, out of 1000 people, we expect 100 to have COVID-19 and 900 to not have COVID-19. Applying the test, we expect:

- TP = 0.95 x 100 = 95
- FP = 0.1 x 900 = 90
- TN = 0.9 x 900 = 810
- FN = 0.05 x 100 = 5

The contingency table for this population is:

Test Positive | Test Negative | Total | |
---|---|---|---|

Have Disease | 95 | 5 | 100 |

Do Not Have Disease | 90 | 810 | 900 |

Total | 185 | 815 | 1000 |

The PPV for this population is:

$$PPV = \frac{95}{185} \approx 0.51$$

The NPV for this population is:

$$NPV = \frac{810}{815} \approx 0.99$$

This means that in this population, if a person tests positive for COVID-19, there is a 51% chance that they actually have COVID-19. If a person tests negative for COVID-19, there is a 99% chance that they do not have COVID-19.

In the low prevalence population, out of 1000 people, we expect 10 to have COVID-19 and 990 to not have COVID-19. Applying the test, we expect:

- TP = 0.95 x 10 = 9.5
- FP = 0.1 x 990 = 99
- TN = 0.9 x 990 = 891
- FN = 0.05 x 10 = 0.5

The contingency table for this population is:

Test Positive | Test Negative | Total | |
---|---|---|---|

Have Disease | 9.5 | 0.5 | 10 |

Do Not Have Disease | 99 | 891 | 990 |

Total | 108.5 | 891.5 | 1000 |

The PPV for this population is:

$$PPV = \frac{9.5}{108.5} \approx 0.09$$

The NPV for this population is:

$$NPV = \frac{891}{891.5} \approx 1$$

This means that in this population, if a person tests positive for COVID-19, there is a 9% chance that they actually have COVID-19. If a person tests negative for COVID-19, there is a 100% chance that they do not have COVID-19.

As we can see, the PPV and NPV vary depending on the prevalence of the disease in the population. Therefore, when interpreting the results of a diagnostic test, we need to consider not only the sensitivity and specificity of the test, but also the prevalence of the disease in the population being tested. This will help us to avoid false positives and false negatives, and to make better clinical decisions.

### Conclusion

Sensitivity, specificity, PPV and NPV are important concepts to understand the accuracy and usefulness of a diagnostic test. Sensitivity and specificity measure the intrinsic properties of a test, while PPV and NPV measure the clinical relevance of a test in a given population. A high sensitivity test is useful for ruling out a disease when the result is negative, while a high specificity test is useful for ruling in a disease when the result is positive. PPV and NPV depend on the prevalence of the disease in the population and indicate the probability of having or not having the disease based on the test result. Ideally, a diagnostic test should have high sensitivity, specificity, PPV and NPV, but this is often not achievable in practice. Therefore, clinicians should be aware of the strengths and limitations of different tests and interpret them with caution and clinical judgment.

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